{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "n33bfLUGmxYe"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "2.1 前向差分"
      ],
      "metadata": {
        "id": "RX3BGTKKm3-a"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GK4VjJ3mlSlf",
        "outputId": "daafe3f6-a07d-4bda-c27c-a8434d45fff7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4.000010000027032\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "\n",
        "def f(x):\n",
        "    return x**2\n",
        "\n",
        "def forward_diff(f, x, h=1e-5):\n",
        "    return (f(x + h) - f(x)) / h\n",
        "\n",
        "x = 2\n",
        "print(forward_diff(f, x))  # 近似 4"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "2.2 中心差分"
      ],
      "metadata": {
        "id": "ovDdNwynm5Lh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def central_diff(f, x, h=1e-5):\n",
        "    return (f(x + h) - f(x - h)) / (2 * h)\n",
        "\n",
        "print(central_diff(f, x))  # 近似 4"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LDF_lrPemBoC",
        "outputId": "8c167a6a-52d5-4c56-d4cc-2e18a3de9741"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4.000000000026205\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "4. 偏导数"
      ],
      "metadata": {
        "id": "DKMLnyRQnPnp"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def f_xy(x, y):\n",
        "    return x**2 + y**2\n",
        "\n",
        "def partial_x(f, x, y, h=1e-5):\n",
        "    return (f(x + h, y) - f(x, y)) / h\n",
        "\n",
        "def partial_y(f, x, y, h=1e-5):\n",
        "    return (f(x, y + h) - f(x, y)) / h\n",
        "\n",
        "x, y = 2, 3\n",
        "print(partial_x(f_xy, x, y))  # 近似 4\n",
        "print(partial_y(f_xy, x, y))  # 近似 6"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ym-5s4J3mG83",
        "outputId": "486d516f-8996-4762-a037-19d38b3a15a7"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4.000010000027032\n",
            "6.000009999951316\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "3. 可视化数值微分"
      ],
      "metadata": {
        "id": "r7mfdQxjnJf_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "x = np.linspace(-2, 2, 100)\n",
        "y = f(x)\n",
        "dy = central_diff(f, x)\n",
        "\n",
        "plt.plot(x, y, label='f(x) = x^2')\n",
        "plt.plot(x, dy, label=\"f'(x)\", linestyle='dashed')\n",
        "plt.legend()\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('Value')\n",
        "plt.title('Function and Derivative')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "hu806sNWmOMM",
        "outputId": "528d2e1b-0510-4f24-8a34-d6026b324f5d"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}